An assessment model for proof comprehension in undergraduate mathematics |
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Authors: | Juan Pablo Mejia-Ramos Evan Fuller Keith Weber Kathryn Rhoads and Aron Samkoff |
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Institution: | (1) Rutgers University, New Brunswick, NJ, USA;(2) Montclair State University, Montclair, NJ, USA |
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Abstract: | Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research
on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper,
we address these issues by presenting a multidimensional model for assessing proof comprehension in undergraduate mathematics.
Building on Yang and Lin’s (Educational Studies in Mathematics 67:59–76, 2008) model of reading comprehension of proofs in high school geometry, we contend that in undergraduate mathematics a proof is
not only understood in terms of the meaning, logical status, and logical chaining of its statements but also in terms of the
proof’s high-level ideas, its main components or modules, the methods it employs, and how it relates to specific examples.
We illustrate how each of these types of understanding can be assessed in the context of a proof in number theory. |
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